Runs Test

Computes the runs test for randomness of the dichotomous (binary) data series x.

runs.test(x, alternative = c("two.sided", "less", "greater"))

Arguments

x

a dichotomous factor.

alternative

indicates the alternative hypothesis and must be one of "two.sided" (default), "less", or "greater". You can specify just the initial letter.

Details

This test searches for randomness in the observed data series x by examining the frequency of runs. A "run" is defined as a series of similar responses.

Note, that by using the alternative "less" the null of randomness is tested against some kind of "under-mixing" ("trend"). By using the alternative "greater" the null of randomness is tested against some kind of "over-mixing" ("mean-reversion").

Missing values are not allowed.

Value

A list with class "htest" containing the following components:

statistic

the value of the test statistic.

p.value

the p-value of the test.

method

a character string indicating what type of test was performed.

data.name

a character string giving the name of the data.

alternative

a character string describing the alternative hypothesis.

References

S. Siegel (1956): Nonparametric Statistics for the Behavioural Sciences, McGraw-Hill, New York.

S. Siegel and N. J. Castellan (1988): Nonparametric Statistics for the Behavioural Sciences, 2nd edn, McGraw-Hill, New York.

Author

A. Trapletti

Examples

x <- factor(sign(rnorm(100)))  # randomness
runs.test(x)
#> 
#> 	Runs Test
#> 
#> data:  x
#> Standard Normal = 0.036315, p-value = 0.971
#> alternative hypothesis: two.sided
#> 

x <- factor(rep(c(-1,1),50))  # over-mixing
runs.test(x)
#> 
#> 	Runs Test
#> 
#> data:  x
#> Standard Normal = 9.8499, p-value < 2.2e-16
#> alternative hypothesis: two.sided
#>